Here in Ontario, the funding comes out of the provincial government, be it for public or Catholic schools, and is levied at the municipal level, so there is very little duplication, as the number and size of schools is demand driven, and there are closures if there is insufficient demand.
There is also a lot of pressure put on boards to cooperate with each other. For example, sharing athletic facilities (public school, catholic school and community centre on one site), and sharing busses.
I am not opposed to multiple school systems, and even more so I am not opposed to multiple schools rather than fewer larger schools.
Multiple school systems (e.g. public English, public French, Catholic English, Catholic French, Protestant English – I recall Ontario having one remaining, private non-religious, private religious) makes it possible to try different approaches and learn from each other, rather than being stuck with one monolithic system.
Smaller schools function better as communities in which the teachers know every child in the school, and significantly reduce the bussing of children. I have seen the American model of huge schools with very large catch basins, and I am not at all impressed.
For example, a town in the middle of nowhere that I frequently visit is consolidating the administration of its English public, French public and public high school, including letting one of the public principals go. This is to avoid school closures that would see students being bussed an hour an a half each way each day to the nearest community. In that same community the Catholic elementary school is looking to hire a principal. As muddled as this is, the result is that there are small local schools of various sorts offering choices of education for the kids, rather than having them spend three hours each day in mobile sardine cans.